utils.jl

using DispatchDoctor: @unstable

function map_dimensions(f::F, args::AbstractDimensions...) where {F<:Function}
    dimension_type = promote_type(typeof(args).parameters...)
    dim_names = dimension_names(dimension_type)
    return new_dimensions(
        dimension_type,
        (
            f((getproperty(arg, dim) for arg in args)...)
            for dim in dim_names
        )...
    )
end
@generated function all_dimensions(f::F, args::AbstractDimensions...) where {F<:Function}
    # Test a function over all dimensions
    output = Expr(:&&)
    dimension_type = promote_type(args...)
    for dim in dimension_names(dimension_type)
        f_expr = :(f())
        for i=1:length(args)
            push!(f_expr.args, :(args[$i].$dim))
        end
        push!(output.args, f_expr)
    end
    return output
end

function Base.promote_rule(::Type{Dimensions{R1}}, ::Type{Dimensions{R2}}) where {R1,R2}
    return Dimensions{promote_type(R1,R2)}
end
function Base.promote_rule(::Type{NoDims{R1}}, ::Type{NoDims{R2}}) where {R1,R2}
    return NoDims{promote_type(R1,R2)}
end
function Base.promote_rule(::Type{NoDims{R1}}, ::Type{D}) where {R1,R2,D<:AbstractDimensions{R2}}
    # The `R1` type is "unused" so we ignore it
    return D
end

# Define all the quantity x quantity promotion rules
"""
    promote_quantity_on_value(Q::Type, T::Type)

Find the next quantity type in the hierarchy that can accommodate the type `T`.
If the current quantity type can already accommodate `T`, then the current type is returned.
For example, `promote_quantity_on_value(Quantity, Float64)` would return `Quantity`, and
`promote_quantity_on_value(RealQuantity, String)` would return `GenericQuantity`.
The user should overload this function to define a custom type hierarchy.

Also see [`promote_quantity_on_quantity`](@ref).
"""
@unstable @inline promote_quantity_on_value(::Type{<:Union{GenericQuantity,Quantity,RealQuantity}}, ::Type{<:Any}) = GenericQuantity
@unstable @inline promote_quantity_on_value(::Type{<:Union{Quantity,RealQuantity}}, ::Type{<:Number}) = Quantity
@unstable @inline promote_quantity_on_value(::Type{<:RealQuantity}, ::Type{<:Real}) = RealQuantity
@unstable @inline promote_quantity_on_value(T, _) = T

"""
    promote_quantity_on_quantity(Q1, Q2)

Defines the type hierarchy for quantities, returning the most specific type
that is compatible with both input quantity types. For example,
`promote_quantity_on_quantity(Quantity, GenericQuantity)` would return `GenericQuantity`,
as it can store both `Quantity` and `GenericQuantity` values.
Similarly, `promote_quantity_on_quantity(RealQuantity, RealQuantity)` would return `RealQuantity`,
as that is the most specific type.

Also see [`promote_quantity_on_value`](@ref).
"""
@unstable @inline promote_quantity_on_quantity(::Type{<:Union{GenericQuantity,Quantity,RealQuantity}}, ::Type{<:Union{GenericQuantity,Quantity,RealQuantity}}) = GenericQuantity
@unstable @inline promote_quantity_on_quantity(::Type{<:Union{Quantity,RealQuantity}}, ::Type{<:Union{Quantity,RealQuantity}}) = Quantity
@unstable @inline promote_quantity_on_quantity(::Type{<:RealQuantity}, ::Type{<:RealQuantity}) = RealQuantity
@unstable @inline promote_quantity_on_quantity(::Type{Q}, ::Type{Q}) where {Q<:UnionAbstractQuantity} = Q

for (type1, _, _) in ABSTRACT_QUANTITY_TYPES, (type2, _, _) in ABSTRACT_QUANTITY_TYPES
    @eval function Base.promote_rule(::Type{Q1}, ::Type{Q2}) where {T1,T2,D1,D2,Q1<:$type1{T1,D1},Q2<:$type2{T2,D2}}
        return with_type_parameters(
            promote_quantity_on_quantity(Q1, Q2),
            promote_type(T1, T2),
            promote_type(D1, D2),
        )
    end
end


# Define promotion rules for all basic numeric types, individually.
# We don't want to define an opinionated promotion on <:Number,
# or even <:AbstractFloat, as it could conflict with other
# abstract number packages which may try to do the same thing.
# (which would lead to ambiguities)
const BASE_NUMERIC_TYPES = Union{
    Bool, Int8, UInt8, Int16, UInt16, Int32, UInt32,
    Int64, UInt64, Int128, UInt128, Float16, Float32,
    Float64, BigFloat, BigInt, ComplexF16, ComplexF32,
    ComplexF64, Complex{BigFloat}, Rational{Int8}, Rational{UInt8},
    Rational{Int16}, Rational{UInt16}, Rational{Int32}, Rational{UInt32},
    Rational{Int64}, Rational{UInt64}, Rational{Int128}, Rational{UInt128},
    Rational{BigInt},
}

for (type, base_type, _) in ABSTRACT_QUANTITY_TYPES
    !(base_type <: Number) && @eval begin
        function Base.convert(::Type{Q}, x::BASE_NUMERIC_TYPES) where {T,D,Q<:$type{T,D}}
            return new_quantity(Q, convert(T, x), D())
        end
    end
    @eval begin
        function Base.promote_rule(::Type{Q}, ::Type{T2}) where {T,D,Q<:$type{T,D},T2<:BASE_NUMERIC_TYPES}
            return with_type_parameters(promote_quantity_on_value(Q, T2), promote_type(T, T2), D)
        end
        function Base.promote_rule(::Type{T2}, ::Type{Q}) where {T,D,Q<:$type{T,D},T2<:BASE_NUMERIC_TYPES}
            return with_type_parameters(promote_quantity_on_value(Q, T2), promote_type(T, T2), D)
        end
    end
end

for (type, _, _) in ABSTRACT_QUANTITY_TYPES
    @eval begin
        function (::Type{T})(q::$type) where {T<:Number}
            q isa T && return q
            @assert iszero(dimension(q)) "$(typeof(q)): $(q) has dimensions! Use `ustrip` instead."
            return convert(T, ustrip(q))
        end
    end
end

"""
    promote_except_value(q1::UnionAbstractQuantity, q2::UnionAbstractQuantity)

This applies a promotion to the quantity type, and the dimension type,
but *not* the value type. This is necessary because sometimes we would
want to multiply a quantity array with a scalar quantity, and wish to use
promotion on the quantity type itself, but don't want to promote to a
single value type.
"""
@inline function promote_except_value(q1::Q1, q2::Q2) where {T1,D1,T2,D2,Q1<:UnionAbstractQuantity{T1,D1},Q2<:UnionAbstractQuantity{T2,D2}}
    Q = promote_type(Q1, Q2)
    D = promote_type(D1, D2)

    Q1_out = with_type_parameters(Q, T1, D)
    Q2_out = with_type_parameters(Q, T2, D)
    return convert(Q1_out, q1), convert(Q2_out, q2)
end
@inline promote_except_value(q1::Q, q2::Q) where {Q<:UnionAbstractQuantity} = (q1, q2)

Base.keys(d::AbstractDimensions) = dimension_names(typeof(d))
Base.getindex(d::AbstractDimensions, k::Symbol) = getfield(d, k)

@generated function dimension_names_equal(::Type{T1}, ::Type{T2}) where {T1,T2}
    # Needs to be a generated function to ensure hardcoded
    return dimension_names(T1) == dimension_names(T2)
end

# Multiplying ranges with units
Base.TwicePrecision{T}(x::T) where {T<:AbstractQuantity} = Base.TwicePrecision{typeof(x)}(x, zero(x))
# TODO: Note that to get RealQuantity working, we have to overload many other functions,
#       which is why we skip it.

# Avoid https://github.com/JuliaLang/julia/issues/56610
for T1 in (AbstractQuantity{<:Real}, Real),
    T2 in (AbstractQuantity{<:Real}, Real),
    T3 in (AbstractQuantity{<:Real}, Real)

    T1 === T2 === T3 === Real && continue

    @eval function Base.:(:)(start::$T1, step::$T2, stop::$T3)
        dimension(start) == dimension(step) || throw(DimensionError(start, step))
        dimension(start) == dimension(stop) || throw(DimensionError(start, stop))
        return range(start, stop, length=length(ustrip(start):ustrip(step):ustrip(stop)))
    end

    if T3 === Real && !(T1 === T2 === Real)
        @eval function Base.:(:)(start::$T1, stop::$T2)
            if !iszero(dimension(start)) || !iszero(dimension(stop))
                error("When creating a range over dimensionful quantities, you must specify a step.")
            end
            return start:1:stop
        end
    end
end

# Compatibility with `.*`
Base.size(q::UnionAbstractQuantity) = size(ustrip(q))
Base.length(q::UnionAbstractQuantity) = length(ustrip(q))
Base.axes(q::UnionAbstractQuantity) = axes(ustrip(q))
Base.iterate(qd::UnionAbstractQuantity, maybe_state...) =
    let subiterate=iterate(ustrip(qd), maybe_state...)
        subiterate === nothing && return nothing
        return new_quantity(typeof(qd), subiterate[1], dimension(qd)), subiterate[2]
    end
Base.ndims(::Type{<:UnionAbstractQuantity{T}}) where {T} = ndims(T)
Base.ndims(q::UnionAbstractQuantity) = ndims(ustrip(q))
Base.broadcastable(q::UnionAbstractQuantity) = new_quantity(typeof(q), Base.broadcastable(ustrip(q)), dimension(q))
for (type, _, _) in ABSTRACT_QUANTITY_TYPES
    @eval Base.getindex(q::$type) = new_quantity(typeof(q), getindex(ustrip(q)), dimension(q))
    @eval Base.getindex(q::$type, i::Integer...) = new_quantity(typeof(q), getindex(ustrip(q), i...), dimension(q))
    type == AbstractGenericQuantity &&
        @eval Base.getindex(q::$type, i...) = new_quantity(typeof(q), getindex(ustrip(q), i...), dimension(q))
end
Base.keys(q::UnionAbstractQuantity) = keys(ustrip(q))

# If atol specified in kwargs, validate its dimensions and then strip units
@inline @unstable function _validate_isapprox(dimcheck, kws)
    if haskey(kws, :atol)
        dimension(dimcheck) == dimension(kws[:atol]) || throw(DimensionError(dimcheck, kws[:atol]))
        return (; kws..., atol=ustrip(kws[:atol]))
    else
        return kws
    end
end

# Numeric checks
for op in (:(<=), :(<), :isless), (type, true_base_type, _) in ABSTRACT_QUANTITY_TYPES
    # Avoid creating overly generic operations on these:
    base_type = true_base_type <: Number ? true_base_type : Number
    @eval begin
        function Base.$(op)(l::$type, r::$type)
            l, r = promote_except_value(l, r)
            dimension(l) == dimension(r) || throw(DimensionError(l, r))
            return $(op)(ustrip(l), ustrip(r))
        end
        function Base.$(op)(l::$type, r::$base_type)
            iszero(dimension(l)) || throw(DimensionError(l, r))
            return $(op)(ustrip(l), r)
        end
        function Base.$(op)(l::$base_type, r::$type)
            iszero(dimension(r)) || throw(DimensionError(l, r))
            return $(op)(l, ustrip(r))
        end
    end
end
for op in (:isequal, :(==)), (type, true_base_type, _) in ABSTRACT_QUANTITY_TYPES
    # Avoid creating overly generic operations on these:
    base_type = true_base_type <: Number ? true_base_type : Number
    @eval begin
        function Base.$(op)(l::$type, r::$type)
            l, r = promote_except_value(l, r)
            return $(op)(ustrip(l), ustrip(r)) && dimension(l) == dimension(r)
        end
        function Base.$(op)(l::$type, r::$base_type)
            return $(op)(ustrip(l), r) && iszero(dimension(l))
        end
        function Base.$(op)(l::$base_type, r::$type)
            return $(op)(l, ustrip(r)) && iszero(dimension(r))
        end
    end
end
for op in (:(<=), :(<), :isless, :isequal, :(==)),
    (t1, _, _) in ABSTRACT_QUANTITY_TYPES,
    (t2, _, _) in ABSTRACT_QUANTITY_TYPES

    t1 == t2 && continue

    @eval function Base.$(op)(l::$t1, r::$t2)
        return $(op)(promote_except_value(l, r)...)
    end
end
# Define isapprox:
for (type, true_base_type, _) in ABSTRACT_QUANTITY_TYPES
    # Avoid creating overly generic operations on these:
    base_type = true_base_type <: Number ? true_base_type : Number
    @eval begin
        function Base.isapprox(l::$type, r::$type; kws...)
            l, r = promote_except_value(l, r)
            dimension(l) == dimension(r) || throw(DimensionError(l, r))
            return isapprox(ustrip(l), ustrip(r); _validate_isapprox(l, kws)...)
        end
        function Base.isapprox(l::$base_type, r::$type; kws...)
            iszero(dimension(r)) || throw(DimensionError(l, r))
            return isapprox(l, ustrip(r); _validate_isapprox(r, kws)...)
        end
        function Base.isapprox(l::$type, r::$base_type; kws...)
            iszero(dimension(l)) || throw(DimensionError(l, r))
            return isapprox(ustrip(l), r; _validate_isapprox(l, kws)...)
        end
    end
    for (type2, _, _) in ABSTRACT_QUANTITY_TYPES

        type == type2 && continue

        @eval function Base.isapprox(l::$type, r::$type2; kws...)
            return isapprox(promote_except_value(l, r)...; kws...)
        end
    end
end


# Simple flags:
for f in (
    :isone, :iszero, :isfinite, :isinf, :isnan, :isreal, :signbit,
    :isempty, :iseven, :isodd, :isinteger, :ispow2
)
    @eval Base.$f(q::UnionAbstractQuantity) = $f(ustrip(q))
end
Base.iszero(d::AbstractDimensions) = all_dimensions(iszero, d)
Base.iszero(::NoDims) = true
Base.:(==)(l::AbstractDimensions, r::AbstractDimensions) = all_dimensions(==, l, r)


# Base.one, typemin, typemax
for f in (:one, :typemin, :typemax)
    @eval begin
        Base.$f(::Type{Q}) where {T,D,Q<:UnionAbstractQuantity{T,D}} = new_quantity(Q, $f(T), D)
        Base.$f(::Type{Q}) where {T,Q<:UnionAbstractQuantity{T}} = $f(with_type_parameters(Q, T, DEFAULT_DIM_TYPE))
        Base.$f(::Type{Q}) where {Q<:UnionAbstractQuantity} = $f(with_type_parameters(Q, DEFAULT_VALUE_TYPE, DEFAULT_DIM_TYPE))
    end
    if f == :one  # Return empty dimensions, as should be multiplicative identity.
        @eval Base.$f(q::Q) where {Q<:UnionAbstractQuantity} = new_quantity(Q, $f(ustrip(q)), one(dimension(q)))
    else
        @eval Base.$f(q::Q) where {Q<:UnionAbstractQuantity} = new_quantity(Q, $f(ustrip(q)), dimension(q))
    end
end
Base.one(::Type{D}) where {D<:AbstractDimensions} = D()
Base.one(::D) where {D<:AbstractDimensions} = one(D)

# Additive identities (zero). We have to invalidate these due to different behavior with conversion
Base.zero(q::Q) where {Q<:UnionAbstractQuantity} = new_quantity(Q, zero(ustrip(q)), dimension(q))
Base.zero(::AbstractDimensions) = error("There is no such thing as an additive identity for a `AbstractDimensions` object, as + is only defined for `UnionAbstractQuantity`.")
Base.zero(::Type{T}) where {T<:UnionAbstractQuantity} = error("Cannot create an additive identity from `Type{<:$(Base.typename(T).wrapper)}`, as the dimensions are unknown. Please use `zero(::$(Base.typename(T).wrapper))` instead.")
Base.zero(::Type{D}) where {D<:AbstractDimensions} = error("There is no such thing as an additive identity for `$(Base.typename(D).wrapper)`, as + is only defined for quantities.")

# Dimensionful 1 (oneunit)
Base.oneunit(q::Q) where {Q<:UnionAbstractQuantity} = new_quantity(Q, oneunit(ustrip(q)), dimension(q))
Base.oneunit(::D) where {D<:AbstractDimensions} = error("There is no such thing as a dimensionful 1 for a `$(Base.typename(D).wrapper)` object, as + is only defined for quantities.")
Base.oneunit(::Type{T}) where {T<:UnionAbstractQuantity} = error("Cannot create a dimensionful 1 from `Type{$(Base.typename(T).wrapper)}` without knowing the dimensions. Please use `oneunit(::$(Base.typename(T).wrapper))` instead.")
Base.oneunit(::Type{D}) where {D<:AbstractDimensions} = error("There is no such thing as a dimensionful 1 for a `$(Base.typename(D).wrapper)` type, as + is only defined for quantities.")

Base.float(::Type{Q}) where {T,D,Q<:UnionAbstractQuantity{T,D}} = with_type_parameters(Q, Base.float(T), D)

Base.show(io::IO, d::AbstractDimensions) =
    let tmp_io = IOBuffer()
        for k in filter(k -> !iszero(d[k]), keys(d))
            print(tmp_io, dimension_name(d, k))
            isone(d[k]) || pretty_print_exponent(tmp_io, d[k])
            print(tmp_io, " ")
        end
        s = String(take!(tmp_io))
        s = replace(s, r"^\s*" => "")
        s = replace(s, r"\s*$" => "")
        print(io, s)
    end
Base.show(io::IO, q::UnionAbstractQuantity{<:Real}) = print(io, ustrip(q), " ", dimension(q))
Base.show(io::IO, q::UnionAbstractQuantity) = print(io, "(", ustrip(q), ") ", dimension(q))

function dimension_name(::AbstractDimensions, k::Symbol)
    default_dimensions = (length="m", mass="kg", time="s", current="A", temperature="K", luminosity="cd", amount="mol")
    return get(default_dimensions, k, string(k))
end

string_rational(x) = isinteger(x) ? string(round(Int, x)) : string(x)
pretty_print_exponent(io::IO, x) = print(io, to_superscript(string_rational(x)))

tryrationalize(::Type{R}, x::R) where {R} = x
tryrationalize(::Type{R}, x::Union{Rational,Integer}) where {R} = convert(R, x)
tryrationalize(::Type{R}, x) where {R} = isinteger(x) ? convert(R, round(Int, x)) : convert(R, rationalize(Int, x))

Base.showerror(io::IO, e::DimensionError) = print(io, "DimensionError: ", e.q1, " and ", e.q2, " have incompatible dimensions")
Base.showerror(io::IO, e::DimensionError{<:Any,Nothing}) = print(io, "DimensionError: ", e.q1, " is not dimensionless")

for (type, _, _) in ABSTRACT_QUANTITY_TYPES, (type2, _, _) in ABSTRACT_QUANTITY_TYPES
    @eval begin
        Base.convert(::Type{Q}, q::$type) where {Q<:$type2} = q
        Base.convert(::Type{Q}, q::$type) where {T,Q<:$type2{T}} = new_quantity(Q, convert(T, ustrip(q)), dimension(q))
        Base.convert(::Type{Q}, q::$type) where {T,D,Q<:$type2{T,D}} = new_quantity(Q, convert(T, ustrip(q)), convert(D, dimension(q)))
    end
    # TODO: This invalidates some methods. But we have to, because
    # the conversion in `number.jl` has a type assertion step, whereas
    # we want to allow things like `convert(Quantity{Float64}, 1.0u"m")`,
    # with the type for the dimensions being inferred.
end

Base.convert(::Type{D}, d::D) where {R,D<:AbstractDimensions{R}} = d
Base.convert(::Type{D}, d::AbstractDimensions{R}) where {R,D<:AbstractDimensions} = with_type_parameters(D, R)(d)
Base.convert(::Type{D}, d::AbstractDimensions) where {R,D<:AbstractDimensions{R}} = D(d)

Base.copy(d::D) where {D<:AbstractDimensions} = map_dimensions(copy, d)
Base.copy(q::Q) where {Q<:UnionAbstractQuantity} = new_quantity(Q, copy(ustrip(q)), copy(dimension(q)))

"""
    ustrip(q::AbstractQuantity)
    ustrip(q::AbstractGenericQuantity)

Remove the units from a quantity.

!!! note

    If using symbolic dimensions, you might also consider using [`ustripexpand`](@ref) to first convert to SI base units before stripping.
"""
@inline ustrip(q::UnionAbstractQuantity) = q.value
ustrip(::AbstractDimensions) = error("Cannot remove units from an `AbstractDimensions` object.")
@inline ustrip(q) = q

"""
    ustrip(unit::UnionAbstractQuantity, q::UnionAbstractQuantity)

Convert quantity `q` to the units specified by `unit`, then strip the units.
This is equivalent to `ustrip(q / unit)`, but also verifies the dimensions are compatible.

# Examples
```jldoctest
julia> ustrip(u"km", 1000u"m")
1.0

julia> ustrip(u"s", 1u"minute")
60.0

julia> ustrip.(u"km", [1000u"m", 2000u"m"])
2-element Vector{Float64}:
 1.0
 2.0
```
"""
@inline function ustrip(unit::UnionAbstractQuantity, q::UnionAbstractQuantity)
    unit, q = promote_except_value(unit, q)
    dimension(unit) == dimension(q) || throw(DimensionError(unit, q))
    return ustrip(q) / ustrip(unit)
end
@inline ustrip(::Type{T}, unit::UnionAbstractQuantity, q::UnionAbstractQuantity) where {T} = convert(T, ustrip(unit, q))

"""
    dimension(q::AbstractQuantity)
    dimension(q::AbstractGenericQuantity)
    dimension(x)

Get the dimensions of a quantity, returning an `AbstractDimensions` object.
"""
dimension(q::UnionAbstractQuantity) = q.dimensions
dimension(d::AbstractDimensions) = d
dimension(aq::AbstractArray{<:UnionAbstractQuantity}) = allequal(dimension.(aq)) ? dimension(first(aq)) : throw(DimensionError(aq[begin], aq[begin+1:end]))
dimension(_) = DEFAULT_DIMENSIONLESS_TYPE()

"""
    isunitless(x)

Return `true` if `x` has no dimensions.

See also [`isdimensionless`](@ref).
"""
isunitless(x) = iszero(dimension(x))

"""
    isdimensionless(x)

Alias for [`isunitless`](@ref).
"""
isdimensionless(x) = isunitless(x)

"""
    unit(q)

Return the multiplicative unit quantity associated with `q`.
"""
unit(q::Q) where {Q<:UnionAbstractQuantity} = oneunit(q)
unit(::Number) = one(DEFAULT_QUANTITY_TYPE)
unit(::Type{<:Number}) = one(DEFAULT_QUANTITY_TYPE)

"""
    upreferred(x)

Compatibility no-op for Unitful.jl-like APIs.
"""
upreferred(x) = x

"""
    ulength(q::AbstractQuantity)
    ulength(q::AbstractGenericQuantity)
    ulength(d::AbstractDimensions)

Get the length dimension of a quantity (e.g., meters^(ulength)).
"""
ulength(q::UnionAbstractQuantity) = ulength(dimension(q))
ulength(d::AbstractDimensions) = d.length

"""
    umass(q::AbstractQuantity)
    umass(q::AbstractGenericQuantity)
    umass(d::AbstractDimensions)

Get the mass dimension of a quantity (e.g., kg^(umass)).
"""
umass(q::UnionAbstractQuantity) = umass(dimension(q))
umass(d::AbstractDimensions) = d.mass

"""
    utime(q::AbstractQuantity)
    utime(q::AbstractGenericQuantity)
    utime(d::AbstractDimensions)

Get the time dimension of a quantity (e.g., s^(utime))
"""
utime(q::UnionAbstractQuantity) = utime(dimension(q))
utime(d::AbstractDimensions) = d.time

"""
    ucurrent(q::AbstractQuantity)
    ucurrent(q::AbstractGenericQuantity)
    ucurrent(d::AbstractDimensions)

Get the current dimension of a quantity (e.g., A^(ucurrent)).
"""
ucurrent(q::UnionAbstractQuantity) = ucurrent(dimension(q))
ucurrent(d::AbstractDimensions) = d.current

"""
    utemperature(q::AbstractQuantity)
    utemperature(q::AbstractGenericQuantity)
    utemperature(d::AbstractDimensions)

Get the temperature dimension of a quantity (e.g., K^(utemperature)).
"""
utemperature(q::UnionAbstractQuantity) = utemperature(dimension(q))
utemperature(d::AbstractDimensions) = d.temperature

"""
    uluminosity(q::AbstractQuantity)
    uluminosity(q::AbstractGenericQuantity)
    uluminosity(d::AbstractDimensions)

Get the luminosity dimension of a quantity (e.g., cd^(uluminosity)).
"""
uluminosity(q::UnionAbstractQuantity) = uluminosity(dimension(q))
uluminosity(d::AbstractDimensions) = d.luminosity

"""
    uamount(q::AbstractQuantity)
    uamount(q::AbstractGenericQuantity)
    uamount(d::AbstractDimensions)

Get the amount dimension of a quantity (e.g., mol^(uamount)).
"""
uamount(q::UnionAbstractQuantity) = uamount(dimension(q))
uamount(d::AbstractDimensions) = d.amount